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Electromagnetic wave propagation in anisotropic media has been widely studied over the last decades since there are several applications where anisotropy plays an important role. This paper presents a procedure to carry out three-dimensional (3D) finite element method (FEM) full-wave simulations of the electromagnetic field in inhomogeneous magnetized plasma of an electron cyclotron resonance ion source (ECRIS). We used COMSOL Multiphysics software and MATLAB to model a cold anisotropic magnetized plasma, described by full-3D non-uniform dielectric tensor, enclosed by the metallic cylindrical cavity where the plasma is formed. A proper mesh generation, exploiting FEM-based COMSOL versatility, allowed us to optimally model ECRIS cavity and microwave waveguide launching structure, with a good computational efficiency and high resolution of the solution especially around the resonance regions. Numerical simulations have been performed in the frequency domain: in the resonance regions especially, the material properties exhibit a spatial variation that leads to a large sparse ill-conditioned matrix which is solved by MUltifrontal Massively Parallel Solver (MUMPS) direct method. We implement a method to perform full-wave simulations considering a cold plasma model for the constitutive relations; the obtained results show that the presence of ECR layer, along with the cavity walls, strongly influences the shape and strength of the electromagnetic field distribution, featuring a strong non-uniformity of the main electromagnetic parameters

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